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I propose to have the category Workarounds added. 

 

There are two instances I can think of that would be beneficial for Maple users that would belong here.  The most recent one http://www.mapleprimes.com/posts/201844-Possible-Bug-In-Maple- and one regarding issues adding the dissipative term to the heat equations http://www.mapleprimes.com/questions/97391-Whats-Wrong-With-Maple-Solution

Users of older versions of Maple or even current Maple versions not yet updated would find this quite useful. 

 

There are some great comments and replies by users that are worth upvoting.   Also choosing as best answer to some posts that were converted from questions would also be helpful here at mapleprimes.

Here's a simple package for drawing knot diagrams and computing the Alexander polynomial. A typical usage case for the AlexanderPolynomial function is when a knot needs to be identified and only a visual representation of the knot is available. Then it's trivial to write down the Dowker sequence by hand and then the sequence can be used as an input for this package. The KnotDiagram function also takes the Dowker sequence as an input.

 

TorusKnot(p, q) and PretzelKnot(p, q, r) are accepted as an input as well and can also be passed to the DowkerNotation function.

 

The algorithm is fairly simple, it works as follows: represent each double point as a quadrilateral (two 'in' vertices and two 'out' vertices); connect the quads according to the Dowker specification; draw the result as a planar graph; erase the sides of each quad and draw its diagonals instead. This draws the intersections corresponding to the double points and guarantees that there are no other intersections. The knot polynomial is then computed from the diagram.

 

The diagrams work fairly well for pretzel knots, but for certain knots they can be difficult to read because some of the quads around the double points can become too small or too skewed. Also, the code doesn't check that the generated quadrilaterals are convex (which is an implicit assumption in the algorithm).

 

knot.txt

knot.mw

read "c:/math/prg/maple/knot.txt"

_m489214528

(1)

with(Knots)

[AlexanderPolynomial, DowkerNotation, KnotDiagram]

(2)

AlexanderPolynomial([6, 8, 10, 2, 4], t)

t^4-t^3+t^2-t+1

(3)

AlexanderPolynomial([4, 10, 14, 12, 2, 8, 6], t)

3*t^2-5*t+3

(4)

AlexanderPolynomial([6, 18, 16, 14, -20, 4, 2, 22, 12, -8, -10], t)

2*t^6-11*t^5+24*t^4-31*t^3+24*t^2-11*t+2

(5)

KnotDiagram([10, 12, -20, -16, -18, 2, 22, 24, -8, -4, -6, 14])

 

AlexanderPolynomial([10, 12, -20, -16, -18, 2, 22, 24, -8, -4, -6, 14], t)

t^10-t^9-t^8+6*t^7-11*t^6+13*t^5-11*t^4+6*t^3-t^2-t+1

(6)

AlexanderPolynomial([4, 8, 10, 16, 2, 18, 20, 22, 6, 14, 12], t)

2*t^6-11*t^5+25*t^4-31*t^3+25*t^2-11*t+2

(7)

DowkerNotation(TorusKnot(5, 4))

[-24, -10, 20, -30, -16, 26, -6, -22, 2, -12, -28, 8, -18, -4, 14]

(8)

KnotDiagram(TorusKnot(5, 4))

 

AlexanderPolynomial(TorusKnot(p, q), t); 1; simplify(subs([p = 5, q = 4], %))

(t^(p*q)-1)*(t-1)/((t^p-1)*(t^q-1))

 

t^12-t^11+t^8-t^6+t^4-t+1

(9)

DowkerNotation(PretzelKnot(3, -4, 5))

[-16, -14, 20, 22, 24, 18, -4, -2, 10, 12, 6, 8]

(10)

KnotDiagram(PretzelKnot(3, -4, 5))

 

AlexanderPolynomial(PretzelKnot(p, q, r), t)

piecewise(p::odd and q::odd and r::odd, piecewise(p*q+p*r+q*r <> -1, (1/4)*signum(p*q+p*r+q*r+1)*((p*q+p*r+q*r)*(t^2-2*t+1)+t^2+2*t+1), 1), AlexanderPolynomial(PretzelKnot(p, q, r), t))

(11)

eval(%, [p = 3, q = -4, r = 5])

2*t^8-3*t^7+2*t^6-t^5+t^4-t^3+2*t^2-3*t+2

(12)

 

Download knot.mw

knot.txt

Mapleprimes should have an option to sort Mapleprimes by the date of the original poster.

The Maple 2015.2 update is now available for Windows and Linux users. It provides official support for Windows 10, connectivity to the latest MATLAB release, support for MapleSim 2015.2, updates to Physics, and a variety of small improvements throughout the product.  It is available through the Check for Updates system, and is also available from our website on the Maple 2015.2 download page.

The Mac update will be released as soon as we have finished fixing the problems on Mac OS X 10.11. We’re working on it.

eithne

We have just released a major update to MapleSim 2015. MapleSim 2015.2 provides a variety of enhancements that make it even easier to create, simulate, and analyze your multidomain, system-level models, including:

  • Advanced diagnostic tools that help you identify the source of problems in your models and simulations, and improve their efficiency and robustness
  • Over 50 new components in the magnetic, thermal, electrical, and signal block libraries
  • A new connections manager that makes it easier to keep track of connections and port variables
  • And more! See What’s New in MapleSim 2015.2 for more information about these and other improvements in MapleSim.

 

We have also updated and expanded the MapleSim 2015 family of products:

  • The new MapleSim CAD Toolbox, which is available as a separate product, helps engineers understand and improve their mechanical designs by making it easy to import CAD models directly into MapleSim and understand how they behave as part of a larger system.
  • MapleSim Connector, for connectivity with Simulink®, and the MapleSim Connector for FMI both generate code that provides more detailed run-time error reporting to assist in trouble-shooting on the target platform
  • Updates to the specialized component libraries MapleSim Battery LibraryMapleSim Driveline Library, and MapleSim Tire Library provide improved modeling power and scope

 

This update is being distributed through the automatic Check for Updates system, and is also available from our website. See MapleSim 2015.2  for details on obtaining this update. This new MapleSim release is available immediately on Windows and Linux, with a Mac version following in the coming days. 

 

eithne

Has anyone tried to run the following in Maple command-line mode (i.e. in terminal window, type "maple" to start it without the graphic interface),

"

expr1:=t1+t2+t3+t4+t5+t6+t7+t8+t9+t10+t11+t12+t13+t14+t15+t16+t17+t18+t19+t20+t21+t22+t0-t0+t23;
expr2:=t1+t2+t3+t4+t5+t6+t7+t8+t9+t10+t11+t12+t13+t14+t15+t16+t17+t18+t19+t20+t21+t22+t0-t0+t23;
print(expr1-expr2);

"

Surprisingly, I didn't get "0" with my Maple 17 (under Linux platform) or 18 (under Mac OSX platform). Can anyone help me confirm this?

As an Arts major at the University of Waterloo, my first day as a co-op student in the Maplesoft marketing department was a bit of a blur. I was hearing a lot of mathematical jargon that I did not understand. Other than a mandatory statistics class in my second year at university, I haven’t taken a math course since high school, over two years ago. I spent my first week as the marketing assistant educating myself about the basics of marketing complex math software. My favourite method for doing this was to read through the Maplesoft user stories. As I read, I was amazed by the variety of customers and the endless applications that Maplesoft products had contributed to. It became apparent that math is a part of every industry and it is in the design of many products. There were a few stories from the robotics industry in particular that really sparked my interest in the software that I now market. 

 

We’ve all seen the futuristic movies where robots gradually get smarter and smarter, developing enough intelligence to control the human race, and eventually, take over the world. As it turns out, Engineered Arts, a UK robotics company, is bringing us one step closer to that reality. Well… they’re maybe not ready for world domination just yet, but they are working on one of the most advanced and human-like robots that the world has seen outside of a Hollywood production, and they are doing this using MapleSim. The first generation of the biologically inspired robot was named RoboThespian. With his ability to speak and sing, he was used to educate, entertain, and investigate new developments in robotics. However, he was largely static. That’s when the engineers began work on generation two of their robot, named Byrun, who has the ability to walk, run, jump, and hop as well as speak and sing. Byrun can even express thousands of different facial features thanks to his projective head display. This makes him even more human-like; scary or cool? I’m thinking a bit of both. If you’re interested in the story, click here to continue reading about it.

 

Another unexpected use of MapleSim was adopted as a joint research project between Ryerson University and McMaster University. I never would have guessed that math software could be applied to the process of human birth. Nevertheless, a group of researchers used MapleSim to simulate induced labour with a Foley Catheter. In short, this is when a small balloon is inserted through the opening of the cervix creating a downward pressure that effectively tricks the cervix into opening for labour to begin. Though the application of this story surprised me, it makes a lot of sense to use modelling software for a research project like this. It’s more efficient to get all of the kinks out of the virtual model in a simulation program before building a physical model that could end up being dysfunctional. According to Dr. James Andrew Smith, a Biomedical Engineering researcher and Assistant Professor in Electrical and Computer Engineering, who is the lead researcher on the project, “Modern engineering has a lot to offer the medical world,” especially when it saves on time and cost. Click here to read more about this story and to watch a video of the finished model.

 

After two months at Maplesoft, I have noticed that I don’t look at things in the same way that I used to. I find myself staring at a toaster and imagining how it was designed. Did the engineers use advanced physical simulation and modeling software to make the most efficient toaster possible? Well, if it can still only toast on one side then, my guess is no! Maplesoft has many more user stories that I haven’t had the chance to read yet. With customers ranging from BMW to Pixar, Maplesoft continues to expand its customer base and adapt its software to support more and more unique applications. I can’t wait to hear what new and unexpected things will be done with the software next!

 

We are looking for enthusiastic Maple users to become Maple Ambassadors, to inspire and educate others about the benefits that Maple brings to education.

 

As an Ambassador, you will have the opportunity to influence the development of Maple through regular meetings with Maplesoft developers, get advance news of upcoming features and products, get assistance with Maple events on your campus, and more. In return, we ask that you do what you are probably already doing – sharing your experiences with Maple, answer questions on forums (like this one!), sharing your Maple applications, providing us with feedback, etc.

 

You can find more information and an application form at Maple Ambassador Program. We’re looking forward to hearing from you!

 

Daniel

Maple Product Management

Here at Maplesoft, we like to foster innovation in technological development. Whether that is finding solutions to global warming, making medical discoveries that save millions, or introducing society to very advanced functional robots, Maplesoft is happy to contribute, support and encourage innovative people and organizations researching these complex topics. This year, we are delighted to have sponsored two contests in the robotics field that provide opportunities to think big and make an impact: Create the Future Design Contest and the International Space Apps Challenge. 

Create the Future Design Contest

Established in 2002, and organized by TechBriefs, the goal of the Create the Future Design Contest is to help engineers bring their product design ideas to life. The overall ‘mission of the contest is to benefit humanity, the environment, and the economy.’ This year, there were a record 1,159 new product ideas submitted by students, engineers, and entrepreneurs from all over the globe. In the machinery/automation/robotics category, which Maplesoft sponsored, the project with the top votes was designed by two engineers who chose to name their innovation CAP Exoskeleton, a type of assistive robotic machine designed to aid the user in walking, squatting, and carrying heavy loads over considerable distances. It can either be used to enhance physical endurance for military purposes or to help the physically impaired perform daily tasks. A contest like Create the Future is a perfect opportunity, for engineers in particular, to learn, explore, and create. 

The CAP Exoskeleton - ©2015 Create the Future Design Contest

 

International Space Apps Challenge

The exploration of space has always been unique in its search for knowledge. The International Space Apps Challenge, a NASA incubator innovation program, is an ‘international mass collaboration focused on space exploration that takes place over 48-hours in cities around the world’. It is a unique global competition where people rally together to find solutions to real world problems, bringing humanity closer to understanding the Earth, the universe, the human race, and robotics. These goals, the organizers believe, can be reached much faster if we combine the power of the seven billion or so brains that occupy the planet, not forgetting the six that are currently orbiting above us aboard the International Space Station. The competition is open to people of all ages and in all fields, including engineers, technologists, scientists, designers, artists, educators, students, entrepreneurs, and so on. With an astounding 13,846 participants from all over the world, several highly innovative solutions were presented. 

Maplesoft sponsored the University of York location in the UK where the winning team of five modeled an app called CropOp, a communication tool that connects the government to local farmers with the goal of providing instantaneous, crucial information regarding pest breakout warnings, extreme weather, and other important updates. This UK-based team believes the quality and quantity of food produced will be improved, especially benefiting the undernourished communities in Africa. Maplesoft supports the Space Apps Challenge because it proves that collaboration makes for bigger and better discoveries that can save millions of people.

 

Donating Maplesoft software for contestants to use is part of the sponsorship. The real delight is to wait and see what innovative concepts they come up with. When we sponsor contests like these, we find it benefits our software as much as it does the participants. Plus, if the contestants can provide solutions to real world issues, well, that benefits everyone! 

ABSTRACT. In this paper we demonstrate how the simulation of dynamic systems engineering has been implemented with graphics software algorithms using maple and MapleSim. Today, many of our researchers the computational modeling performed by inserting a piece of code from static work; with these packages we have implemented through the automation components of kinematics and dynamics of solids simple to complex.

It is very important to note that once developed equations study; recently we can move to the simulation; to thereby start the physical construction of the system. We will use mathematical and computational methods using the embedded buttons which lie in the dynamics leaves and viewing platform cloud of Maplesoft and power MapleNet for online evaluation of specialists in the area. Finally they will see some work done; which integrate various mechanical and computational concepts implemented for companies in real time and pattern of credibility.

 

Selasi_2015.pdf

(in spanish)

 

Lenin Araujo Castillo

 

 

Transitioning to Jordan Form...

November 02 2015 rlopez 1637 Maple 2015
5
10

I have two linear algebra texts [1, 2]  with examples of the process of constructing the transition matrix Q that brings a matrix A to its Jordan form J. In each, the authors make what seems to be arbitrary selections of basis vectors via processes that do not seem algorithmic. So recently, while looking at some other calculations in linear algebra, I decided to revisit these calculations in as orderly a way as possible.

 

First, I needed a matrix A with a prescribed Jordan form. Actually, I started with a Jordan form, and then constructed A via a similarity transform on J. To avoid introducing fractions, I sought transition matrices P with determinant 1.

 

Let's begin with J, obtained with Maple's JordanBlockMatrix command.

 

• 

Tools_Load Package: Linear Algebra

Loading LinearAlgebra

J := JordanBlockMatrix([[2, 3], [2, 2], [2, 1]])

Matrix([[2, 1, 0, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 1, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 2]])

 

``

The eigenvalue lambda = 2 has algebraic multiplicity 6. There are sub-blocks of size 3×3, 2×2, and 1×1. Consequently, there will be three eigenvectors, supporting chains of generalized eigenvectors having total lengths 3, 2, and 1. Before delving further into structural theory, we next find a transition matrix P with which to fabricate A = P*J*(1/P).

 

The following code generates random 6×6 matrices of determinant 1, and with integer entries in the interval [-2, 2]. For each, the matrix A = P*J*(1/P) is computed. From these candidates, one A is then chosen.

 

L := NULL:

 

 

After several such trials, the matrix A was chosen as

 

A := Matrix(6, 6, {(1, 1) = -8, (1, 2) = -8, (1, 3) = 4, (1, 4) = -8, (1, 5) = -1, (1, 6) = 5, (2, 1) = -1, (2, 2) = 3, (2, 3) = 1, (2, 4) = -2, (2, 5) = 2, (2, 6) = -1, (3, 1) = -13, (3, 2) = -9, (3, 3) = 8, (3, 4) = -11, (3, 5) = 1, (3, 6) = 5, (4, 1) = 3, (4, 2) = 3, (4, 3) = -1, (4, 4) = 4, (4, 5) = 1, (4, 6) = -2, (5, 1) = 7, (5, 2) = 5, (5, 3) = -3, (5, 4) = 6, (5, 5) = 2, (5, 6) = -3, (6, 1) = -6, (6, 2) = -2, (6, 3) = 3, (6, 4) = -7, (6, 5) = 2, (6, 6) = 3})

 

 

for which the characteristic and minimal polynomials are

 

factor(CharacteristicPolynomial(A, lambda))

(lambda-2)^6

factor(MinimalPolynomial(A, lambda))

(lambda-2)^3

 

 

So, if we had started with just A, we'd now know that the algebraic multiplicity of its one eigenvalue lambda = 2 is 6, and there is at least one 3×3 sub-block in the Jordan form. We would not know if the other sub-blocks were all 1×1, or a 1×1 and a 2×2, or another 3×3. Here is where some additional theory must be invoked.

``

The null spaces M[k] of the matrices (A-2*I)^k are nested: `&sub;`(`&sub;`(M[1], M[2]), M[3]) .. (), as depicted in Figure 1, where the vectors a[k], k = 1, () .. (), 6, are basis vectors.

 

Figure 1   The nesting of the null spaces M[k] 

 

 

The vectors a[1], a[2], a[3] are eigenvectors, and form a basis for the eigenspace M[1]. The vectors a[k], k = 1, () .. (), 5, form a basis for the subspace M[2], and the vectors a[k], k = 1, () .. (), 6, for a basis for the space M[3], but the vectors a[4], a[5], a[6] are not yet the generalized eigenvectors. The vector a[6] must be replaced with a vector b[6] that lies in M[3] but is not in M[2]. Once such a vector is found, then a[4] can be replaced with the generalized eigenvector `&equiv;`(b[4], (A-2*I)^2)*b[6], and a[1] can be replaced with `&equiv;`(b[1], A-2*I)*b[4]. The vectors b[1], b[4], b[6] are then said to form a chain, with b[1] being the eigenvector, and b[4] and b[6] being the generalized eigenvectors.

 

If we could carry out these steps, we'd be in the state depicted in Figure 2.

 

Figure 2   The null spaces M[k] with the longest chain determined

 

 

Next, basis vector a[5] is to be replaced with b[5], a vector in M[2] but not in M[1], and linearly independent of b[4]. If such a b[5] is found, then a[2] is replaced with the generalized eigenvector `&equiv;`(b[2], A-2*I)*b[5]. The vectors b[2] and b[5] would form a second chain, with b[2] as the eigenvector, and b[5] as the generalized eigenvector.

``

Define the matrix C = A-2*I by the Maple calculation

 

C := A-2

Matrix([[-10, -8, 4, -8, -1, 5], [-1, 1, 1, -2, 2, -1], [-13, -9, 6, -11, 1, 5], [3, 3, -1, 2, 1, -2], [7, 5, -3, 6, 0, -3], [-6, -2, 3, -7, 2, 1]])

 

``

and note

 

N := convert(NullSpace(C), list)

[Vector(6, {(1) = 1/2, (2) = 1/2, (3) = 1, (4) = 0, (5) = 0, (6) = 1}), Vector(6, {(1) = -1/2, (2) = -1/2, (3) = -2, (4) = 0, (5) = 1, (6) = 0}), Vector(6, {(1) = -2, (2) = 1, (3) = -1, (4) = 1, (5) = 0, (6) = 0})]

NN := convert(LinearAlgebra:-NullSpace(C^2), list)

[Vector(6, {(1) = 2/5, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 1}), Vector(6, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 1, (6) = 0}), Vector(6, {(1) = -1, (2) = 0, (3) = 0, (4) = 1, (5) = 0, (6) = 0}), Vector(6, {(1) = 2/5, (2) = 0, (3) = 1, (4) = 0, (5) = 0, (6) = 0}), Vector(6, {(1) = -3/5, (2) = 1, (3) = 0, (4) = 0, (5) = 0, (6) = 0})]

 

``

The dimension of M[1] is 3, and of M[2], 5. However, the basis vectors Maple has chosen for M[2] do not include the exact basis vectors chosen for M[1].

 

We now come to the crucial step, finding b[6], a vector in M[3] that is not in M[2] (and consequently, not in M[1] either). The examples in [1, 2] are simple enough that the authors can "guess" at the vector to be taken as b[6]. What we will do is take an arbitrary vector in M[3] and project it onto the 5-dimensional subspace M[2], and take the orthogonal complement as b[6].

``

A general vector in M[3] is

 

Z := `<,>`(u || (1 .. 6))

Vector[column]([[u1], [u2], [u3], [u4], [u5], [u6]])

 

``

A matrix that projects onto M[2] is

 

P := ProjectionMatrix(NN)

Matrix([[42/67, -15/67, 10/67, -25/67, 0, 10/67], [-15/67, 58/67, 6/67, -15/67, 0, 6/67], [10/67, 6/67, 63/67, 10/67, 0, -4/67], [-25/67, -15/67, 10/67, 42/67, 0, 10/67], [0, 0, 0, 0, 1, 0], [10/67, 6/67, -4/67, 10/67, 0, 63/67]])

 

``

The orthogonal complement of the projection of Z onto M[2] is then -P*Z+Z. This vector can be simplified by choosing the parameters in Z appropriately. The result is taken as b[6].

 

b[6] := 67*(eval(Z-Typesetting:-delayDotProduct(P, Z), Equate(Z, UnitVector(1, 6))))*(1/5)

Vector[column]([[5], [3], [-2], [5], [0], [-2]])

NULL

 

``

The other two members of this chain are then

 

b[4] := Typesetting:-delayDotProduct(C, b[6])

Vector[column]([[-132], [-12], [-169], [40], [92], [-79]])

b[1] := Typesetting:-delayDotProduct(C, b[4])

Vector[column]([[-67], [134], [67], [67], [0], [134]])

 

``

A general vector in M[2] is a linear combination of the five vectors that span the null space of C^2, namely, the vectors in the list NN. We obtain this vector as

 

ZZ := add(u || k*NN[k], k = 1 .. 5)

Vector[column]([[(2/5)*u1-u3+(2/5)*u4-(3/5)*u5], [u5], [u4], [u3], [u2], [u1]])

 

``

A vector in M[2] that is not in M[1] is the orthogonal complement of the projection of ZZ onto the space spanned by the eigenvectors spanning M[1] and the vector b[4]. This projection matrix is

 

PP := LinearAlgebra:-ProjectionMatrix(convert(`union`(LinearAlgebra:-NullSpace(C), {b[4]}), list))

Matrix([[69/112, -33/112, 19/112, -17/56, 0, 19/112], [-33/112, 45/112, 25/112, 13/56, 0, 25/112], [19/112, 25/112, 101/112, 1/56, 0, -11/112], [-17/56, 13/56, 1/56, 5/28, 0, 1/56], [0, 0, 0, 0, 1, 0], [19/112, 25/112, -11/112, 1/56, 0, 101/112]])

 

``

The orthogonal complement of ZZ, taken as b[5], is then

 

b[5] := 560*(eval(ZZ-Typesetting:-delayDotProduct(PP, ZZ), Equate(`<,>`(u || (1 .. 5)), LinearAlgebra:-UnitVector(4, 5))))

Vector[column]([[-9], [-59], [17], [58], [0], [17]])

 

``

Replace the vector a[2] with b[2], obtained as

 

b[2] := Typesetting:-delayDotProduct(C, b[5])

Vector[column]([[251], [-166], [197], [-139], [-112], [-166]])

 

 

The columns of the transition matrix Q can be taken as the vectors b[1], b[4], b[6], b[2], b[5], and the eigenvector a[3]. Hence, Q is the matrix

 

Q := `<|>`(b[1], b[4], b[6], b[2], b[5], N[3])

Matrix([[-67, -132, 5, 251, -9, -2], [134, -12, 3, -166, -59, 1], [67, -169, -2, 197, 17, -1], [67, 40, 5, -139, 58, 1], [0, 92, 0, -112, 0, 0], [134, -79, -2, -166, 17, 0]])

 

``

Proof that this matrix Q indeed sends A to its Jordan form consists in the calculation

 

1/Q.A.Q = Matrix([[2, 1, 0, 0, 0, 0], [0, 2, 1, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 1, 0], [0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 2]])``

 

NULL

The bases for M[k], k = 1, 2, 3, are not unique. The columns of the matrix Q provide one set of basis vectors, but the columns of the transition matrix generated by Maple, shown below, provide another.

 

JordanForm(A, output = 'Q')

Matrix([[-5, -43/5, -9/5, 7/5, -14/5, -3/5], [10, -4/5, -6/25, 1/5, -6/25, -3/25], [5, -52/5, -78/25, 13/5, -78/25, -39/25], [5, 13/5, 38/25, -2/5, 38/25, 4/25], [0, 6, 42/25, -1, 42/25, 21/25], [10, -29/5, -11/25, 1/5, -11/25, 7/25]])

 

``

I've therefore added to my to-do list the investigation into Maple's algorithm for determining an appropriate set of basis vectors that will support the Jordan form of a matrix.

 

References

 

NULL

[1] Linear Algebra and Matrix Theory, Evar Nering, John Wiley and Sons, Inc., 1963

[2] Matrix Methods: An Introduction, Richard Bronson, Academic Press, 1969

 

NULL

``

Download JordanForm_blog.mw

There are few ways to determine the day of the year.  The first way I show here is a bug.

with(Finance):
FormatDate("Aug-4-2015","%j")
                                             "%j"

it was described on the help page that the options can be of the form of any described in StringTools[ParseTime] of which %j did not work.  Fortunately there's other ways.

with(StringTools):
ParseTime("%m-%d-%Y", "8-4-2015"):-yearDay
                                                                       216

with(Finance):
DayCount("jan-1-2015", "aug-4-2015")+1
                                                                  216

 

 

                                                              

 

 

Some time ago, @marc005 asked how he could send an email from the Maple command line.

Why would you want to do this? Using Maple's functionality, you could programatically construct an email - perhaps with the results of a computation - and email it yourself or someone else.

I originally posted a solution that involved communicating with a locally-installed SMTP server using the Sockets package. But of course, you need to set up an SMTP server and ensure the appropriate ports are open.

I recently found a better solution. Mailgun (http://mailgun.com) is a free email delivery service with an web-based API. You can communicate with this API via the URL package; simply send Mailgun a URL:-Post() message that contains account-specific information, and the text of your email.

The general steps and Maple commands are given below, and you can download the worksheet here.

Note: Maplesoft have no affiliation with Mailgun.

Step 1:
Sign up for a free Mailgun account.

Step 2:
In your Mailgun account, go to the Domains section - it should look like the screengrab below (account-specific information has been blanked).

Note down the API Base URL and the API key.

  • the API Base URL looks like https://api.mailgun.net/v3/sandboxXXXXXXXXXXXXXXXXXXXXXXXXXXX.mailgun.org.  
  • •the API Key looks like key-XXXXXXXXXXXXXXXXXXXXXXXXXX

Step 3:

In Maple, define strings containing your own API Base URL and API Key. Also, define the recipient's email address, the email you want the recipient to reply to, the email subject and email body.

>restart:
>APIBaseURL := "https://api.mailgun.net/v3/sandboxXXXXXXXXXXXXXXXXXXXXXXXX.mailgun.org":
>APIKey:="key-XXXXXXXXXXXXXXXXXXXXXXXX":
>toEmail := "xxxxx@xxxxxx.com":
>fromEmail:="First Last <FirstLast@Domain.com>":
>subject:= "Email Subject Goes Here":
>emailBody := "I'd rather have a bottle in front of me than a frontal lobotomy":

Step 4:
Run the following code

> URL:-Post(cat(APIBaseURL,"/messages"),[
"from"=fromEmail,"to"=toEmail,
"subject"=subject,
"text"= emailBody],
user="api",password=APIKey);

If you've successfully sent the email, you should see something like this (account-specific information is blanked out)

You can also send HTML emails by replacing the "text" line with "html" = str, where str is a string with your HTML code.

For those who are running Maple and/or MapleSim on the Mac, and who may have missed an earlier question on this site, we wanted to let you know that there are some problems with running Maple and MapleSim on the new Mac OS, Mac OS X 10.11 (El Capitan). We’re working on a solution, which we expect will be ready in a few weeks. We’ll keep you posted, but in the meantime, please delay updating your Mac OS for now to avoid problems.

 

eithne

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